Efficient estimation of population variance of a sensitive variable using a new scrambling response model

Abstract

This study introduces a pioneering scrambling response model tailored for handling sensitive variables. Subsequently, a generalized estimator for variance estimation, relying on two auxiliary information sources, is developed following this novel model. Analytical expressions for bias, mean square error, and minimum mean square error are meticulously derived up to the first order of approximation, shedding light on the estimator’s statistical performance. Comprehensive simulation experiments and empirical analysis unveil compelling results. The proposed generalized estimator, operating under both scrambling response models, consistently exhibits minimal mean square error, surpassing existing estimation techniques. Furthermore, this study evaluates the level of privacy protection afforded to respondents using this model, employing a robust framework of simulations and empirical studies.

A novel randomized scrambling technique for mean estimation of a finite population

“…In this regard, the study of Gupta et al [ 21 ] motivated survey researchers to explore efficient estimators of variance by using randomized scrambling models. The studies of Aloraini et al [ 22 ], Saleem et al [ 23 ] and Kumar et al [ 24 ] presented efficient estimators of population variance under randomized models. Azeem et al [ 25 ] also utilized a linear scrambling technique to suggest a new estimator of population variance.…”